The steps of the PDD algorithm using BSUM to solve the optimization problem in (REF ) are described in Algorithm REF . blackThe steps of the basic PDD method in which the dual variables and the penalty parameter are updated, in addition to a detailed convergence analysis for this scheme are provided in [1]}. Specifically, it is shown that under appropriate conditions, the sequence of \(\mathbf {t}^{k}\in \mathcal {S}\)  generated by the PDD method tends to a KKT point of the main problem. In Algorithm 1, the update method for the dual variable \(\lambda _a\)  in the \(k\) th iteration is as follows
\(\lambda _a^{k}=\lambda _{a}^{k-1}+\frac{1}{\gamma }(\mathbf {a}-\bar{\mathbf {a}}).\) 
